The character of the metaplectic representation and the character formula for certain representations of an almost algebraic Lie group over a \(p\)-adic field
type: Item
instance of: scholarly article
title: The character of the metaplectic representation and the character formula for certain representations of an almost algebraic Lie group over a \(p\)-adic field
zbMATH Open document ID: 0948.22017
author: Khemais Maktouf
published in: Journal of Functional Analysis
publication date: 2000-11-12T00:00:00Z
review text: It is known that the character of the Weil representation of a metaplectic group over a local field \(k\) is a locally integrable function, which is smooth on the set of regular semi-simple elements. It has been computed in the case \(k = {\mathbb R}\). In the present article \(k\) is \(p\)-adic of characteristic zero. An explicit formula is given for the character of the metaplectic representation as a locally constant function on an open set which is larger than the set of regular semi-simple elements. The method consists mainly of Harish-Chandra's descent and the explicit calculation of the character of representations of the Heisenberg group. In the second half of the paper the former results are used to prove a character formula in the neighbourhood of a semi-simple element for certain irreducible unitary representations of almost algebraic \(p\)-adic groups.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 1309116
zbMATH Keywords: character
zbMATH Keywords: Weil representation
zbMATH Keywords: metaplectic group
zbMATH Keywords: irreducible unitary representations
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
full work available at URL: jfan.1999.3394
OpenAlex ID: W2071923800
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DOI: 10.1006/JFAN.1999.3394
description: scientific article; zbMATH DE number 1309116